1 Introduction

This paper contains estimates for the effective reproduction number \(R_{t,m}\) over time \(t\) in various provinces \(m\) of South Africa. This is done using the methodology as described in [1]. These have been implemented in R using EpiEstim package [2] which is what is used here. The methodolgy and assumptions are described in more detail here.

This paper and it’s results should be updated roughly daily and is available online.

As this paper is updated over time this section will summarise significant changes. The code producing this paper is tracked using Git. The Git commit hash for this project at the time of generating this paper was c3b9cdd6ce351b95596a9ade67db014572999791.

2 Data

Data is downloaded from the Git repository associated with [3]. This contains the daily cases and deaths reported by the NICD for South Africa by province. The data is somewhat problematic as it does not contain data by date of test or date of death but by reporting date. It’s not clear what the reporting delays are and they may be significant (especially for the deaths).

In the case data file row 21 and 32 contain no provincial details. We estimated it by spreading the national total to the provinces in proportion to the combined mixture of the prior day and the next day.

Further fixes are applied to both case and death data:

  1. Scale up the per province data for unknown values.
  2. This results in provincial data which are not whole numbers. These are rounded to the nearest whole number.
  3. A SA column is added as the sum of the new per province data.
  4. Data is formatted and disaggregated such that item represents the incremental cases or deaths rather than cumulative figures.
  5. Data is filled with data (albeit with 0 cases or deaths) for all dates in the range.
  6. Any incremental case or death counts that are negative are set to zero.
  7. New cumulative figures are calculated.

3 Methodology

The methodology is described in detail here.

4 Results

4.1 Cases and Deaths

Below we plot cumulative case count on a log scale by province:

Below we plot the cumulative deaths by province on a log scale:

4.2 Current \(R_{t,m}\) estimates by Province

Below current (last weekly) \(R_{t,m}\) estimates are tabulated.

Estimated Effective Reproduction Number by Province
province Estimated Type Count (Last Week) Week Ending R - Lower CI R - Mean R - Uppper CI
EC cases 11,239 2020-12-12 1.1 1.1 1.1
EC deaths 545 2020-12-12 1.4 1.6 1.8
FS cases 437 2020-12-12 1.2 1.3 1.4
FS deaths 72 2020-12-12 0.7 0.9 1.1
GP cases 7,035 2020-12-12 1.7 2.0 2.3
GP deaths 69 2020-12-12 1.4 1.8 2.3
KZN cases 8,806 2020-12-12 1.8 2.1 2.4
KZN deaths 65 2020-12-12 1.0 1.3 1.6
LP cases 404 2020-12-12 1.4 1.5 1.7
LP deaths 2 2020-12-12 0.1 0.4 0.9
MP cases 526 2020-12-12 1.2 1.3 1.5
MP deaths 0 2020-12-12 0.4 1.4 3.2
NC cases 279 2020-12-12 1.0 1.1 1.2
NC deaths 23 2020-12-12 0.9 1.3 1.9
NW cases 529 2020-12-12 1.6 1.8 2.0
NW deaths 0 2020-12-12 0.0 0.1 0.3
WC cases 13,261 2020-12-12 1.4 1.5 1.6
WC deaths 263 2020-12-12 1.2 1.4 1.6
SA cases 42,516 2020-12-12 1.4 1.5 1.6
SA deaths 1,039 2020-12-12 1.3 1.4 1.5
Estimated Effective Reproduction Number by Province

Estimated Effective Reproduction Number by Province

4.3 Maps of Effective Reproduction Number

Below estimates of the reproductive number is plotted on maps of South Africa [4].

4.3.1 Cases

Estimated effective reproduction number based on cases

Estimated effective reproduction number based on cases

4.3.2 Deaths

Estimated effective reproduction number based on deaths

Estimated effective reproduction number based on deaths

4.4 Estimated Effective Reproduction Number for South Africa over Time

Below we plot results for South Africa as a whole.

Estimated Effective Reproduction Number for South Africa over Time

Estimated Effective Reproduction Number for South Africa over Time

4.5 Estimated Effective Reproduction Number for Provinces over Time

Below we plot results for each province. We filter out weeks where the upper end of confidence interval for \(R_{t,m}\) exceeds 4.

4.5.1 Eastern Cape

Estimated Effective Reproduction Number for Eastern Cape over Time

Estimated Effective Reproduction Number for Eastern Cape over Time

4.5.2 Free State

Estimated Effective Reproduction Number for Free State over Time

Estimated Effective Reproduction Number for Free State over Time

4.5.3 Gauteng

Estimated Effective Reproduction Number for Gauteng over Time

Estimated Effective Reproduction Number for Gauteng over Time

4.5.4 KwaZulu-Natal

Estimated Effective Reproduction Number for KwaZulu-Natal over Time

Estimated Effective Reproduction Number for KwaZulu-Natal over Time

4.5.5 Limpopo

Estimated Effective Reproduction Number for Limpopo over Time

Estimated Effective Reproduction Number for Limpopo over Time

4.5.6 Mpumalanga

Estimated Effective Reproduction Number for Mpumalanga over Time

Estimated Effective Reproduction Number for Mpumalanga over Time

4.5.7 Northern Cape

Estimated Effective Reproduction Number for Northern Cape over Time

Estimated Effective Reproduction Number for Northern Cape over Time

4.5.8 North West

Estimated Effective Reproduction Number for Gauteng over Time

Estimated Effective Reproduction Number for Gauteng over Time

4.5.9 Western Cape

Estimated Effective Reproduction Number for Western Cape over Time

Estimated Effective Reproduction Number for Western Cape over Time

4.6 Detailed Results

Detailed output for all provinces are saved to a comma-separated value file. The file can be found here.

5 Discussion

Limitation of this method to estimate \(R_{t,m}\) are noted in [1]

  • It’s sensitive to changes in transmissibility, changes in contact patterns, depletion of the susceptible population and control measures.
  • It relies on an assumed generation interval assumptions.
  • The size of the time window can affect the volatility of results.
  • Results are time lagged with regards to true infection, more so in the case of the use of deaths.
  • It’s sensitive to changes in case (or death) detection.
  • The generation interval may change over time.

Further to the above the estimates are made under assumption that the cases and deaths are reported consistently over time. For cases this means that testing needs to be at similar levels and reported with similar lag. Should these change rapidly over an interval of a few weeks the above estimates of the effective reproduction numbers would be biased. For example a rapid expansion of testing over the last 3 weeks would results in overestimating recent effective reproduction numbers. Similarly any changes in reporting (over time and underreporting) of deaths would also bias estimates of the reproduction number estimated using deaths. It may well be that some catch-up in reported deaths is exaggerating the estimates for October.

Estimates for the reproduction number are plotted in time period in which the relevant measure is recorded. Though in reality the infections giving rise to those estimates would have occurred roughly between a week to 4 weeks earlier depending on whether it was cases or deaths. These figures have not been shifted back.

Despite these limitation we believe the ease of calculation of this method and the ability to use multiple sources makes it useful as a monitoring tool.

Having said all the above it would appear that the effective reproduction number was reasonably high in South Africa from middle April to middle July. From middle July the figures seems to have decreased well below 1. However since middle September figures have been near 1 and in October these seem to have shifted above 1.

6 Author

This report was prepared by Louis Rossouw. Please get in contact with Louis Rossouw if you have comments or wish to receive this regularly.

Louis Rossouw
Head of Research & Analytics
Gen Re | Life/Health Canada, South Africa, Australia, NZ, UK & Ireland
Email: LRossouw@GenRe.com Mobile: +27 71 355 2550

The views in this document represents that of the author and may not represent those of Gen Re. Also note that given the significant uncertainty involved with the parameters, data and methodology care should be taken with these numbers and any use of these numbers.

References

[1] A. Cori, N. M. Ferguson, C. Fraser, and S. Cauchemez, “A new framework and software to estimate time-varying reproduction numbers during epidemics,” American Journal of Epidemiology, vol. 178, no. 9, pp. 1505–1512, Sep. 2013, doi: 10.1093/aje/kwt133. [Online]. Available: https://doi.org/10.1093/aje/kwt133

[2] A. Cori, EpiEstim: A package to estimate time varying reproduction numbers from epidemic curves. 2013 [Online]. Available: https://CRAN.R-project.org/package=EpiEstim

[3] V. Marivate et al., “Coronavirus disease (COVID-19) case data - South Africa.” Zenodo, 21-Mar-2020 [Online]. Available: https://zenodo.org/record/3888499. [Accessed: 26-Oct-2020]

[4] OCHA, “South africa - subnational administrative boundaries,” Dec. 2018 [Online]. Available: https://data.humdata.org/dataset/south-africa-admin-level-1-boundaries